Information on Result #629411
Linear OA(2170, 186, F2, 81) (dual of [186, 16, 82]-code), using concatenation of two codes based on
- linear OA(454, 62, F4, 40) (dual of [62, 8, 41]-code), using
- 3 times truncation [i] based on linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- 3 times truncation [i] based on linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
- linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2170, 186, F2, 80) (dual of [186, 16, 81]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2170, 186, F2, 79) (dual of [186, 16, 80]-code) | [i] | ||
| 3 | Linear OA(2170, 186, F2, 78) (dual of [186, 16, 79]-code) | [i] | ||
| 4 | Linear OA(2170, 186, F2, 77) (dual of [186, 16, 78]-code) | [i] | ||
| 5 | Linear OA(2170, 186, F2, 76) (dual of [186, 16, 77]-code) | [i] | ||
| 6 | Linear OA(2180, 196, F2, 81) (dual of [196, 16, 82]-code) | [i] | Code Embedding in Larger Space | |
| 7 | Linear OA(2181, 197, F2, 81) (dual of [197, 16, 82]-code) | [i] | ||
| 8 | Linear OA(2182, 198, F2, 81) (dual of [198, 16, 82]-code) | [i] | ||
| 9 | Linear OA(2169, 185, F2, 80) (dual of [185, 16, 81]-code) | [i] | Truncation | |
| 10 | Linear OA(2168, 184, F2, 79) (dual of [184, 16, 80]-code) | [i] | ||
| 11 | Linear OA(2166, 182, F2, 77) (dual of [182, 16, 78]-code) | [i] | ||
| 12 | Linear OA(2165, 181, F2, 76) (dual of [181, 16, 77]-code) | [i] | ||
| 13 | Linear OA(2163, 179, F2, 74) (dual of [179, 16, 75]-code) | [i] | ||
| 14 | Linear OA(2162, 178, F2, 73) (dual of [178, 16, 74]-code) | [i] | ||
| 15 | Linear OA(2160, 176, F2, 71) (dual of [176, 16, 72]-code) | [i] | ||
| 16 | Linear OA(2159, 175, F2, 70) (dual of [175, 16, 71]-code) | [i] | ||
| 17 | Linear OA(2157, 173, F2, 68) (dual of [173, 16, 69]-code) | [i] | ||
| 18 | Linear OOA(2170, 93, F2, 2, 81) (dual of [(93, 2), 16, 82]-NRT-code) | [i] | OOA Folding | |
| 19 | Linear OOA(2170, 62, F2, 3, 81) (dual of [(62, 3), 16, 82]-NRT-code) | [i] | ||
| 20 | Linear OOA(2170, 37, F2, 5, 81) (dual of [(37, 5), 15, 82]-NRT-code) | [i] | ||